MinT - Information on Result #2668200

Information on Result #2668200

Linear OOA(2²⁰⁶, 2742, F₂, 3, 30) (dual of [(2742, 3), 8020, 31]-NRT-code), using 2² times duplication based on linear OOA(2²⁰⁴, 2742, F₂, 3, 30) (dual of [(2742, 3), 8022, 31]-NRT-code), using

strength reduction [i] based on linear OOA(2²⁰⁴, 2742, F₂, 3, 31) (dual of [(2742, 3), 8022, 32]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2²⁰⁴, 8226, F₂, 31) (dual of [8226, 8022, 32]-code), using
  - 2 times code embedding in larger space [i] based on linear OA(2²⁰², 8224, F₂, 31) (dual of [8224, 8022, 32]-code), using
    - constructionÂ X applied to C_e(30) âŠ‚ C_e(26) [i] based on
      1. linear OA(2¹⁹⁶, 8192, F₂, 31) (dual of [8192, 7996, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      2. linear OA(2¹⁷⁰, 8192, F₂, 27) (dual of [8192, 8022, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 8191Â = 2¹³âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
      3. linear OA(2⁶, 32, F₂, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
        Reedâ€“Muller code RM(1,5) [i]
        caps in base bÂ =Â 2 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2²⁰⁶, 2326, F₂, 4, 30) (dual of [(2326, 4), 9098, 31]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
2	Linear OOA(2²⁰⁶, 2326, F₂, 5, 30) (dual of [(2326, 5), 11424, 31]-NRT-code)	[i]
3	Linear OOA(2²⁰⁶, 2326, F₂, 6, 30) (dual of [(2326, 6), 13750, 31]-NRT-code)	[i]
4	Linear OOA(2²⁰⁶, 2326, F₂, 7, 30) (dual of [(2326, 7), 16076, 31]-NRT-code)	[i]
5	Linear OOA(2²⁰⁶, 2326, F₂, 8, 30) (dual of [(2326, 8), 18402, 31]-NRT-code)	[i]
6	Digital (176, 206, 2326)-net over F₂	[i]